CONFORMAL VECTOR FIELDS AND TOTALLY UMBILIC HYPERSURFACES

Title & Authors
CONFORMAL VECTOR FIELDS AND TOTALLY UMBILIC HYPERSURFACES
Kim, Dong-Soo; Kim, Seon-Bu; Kim, Young-Ho; Park, Seong-Hee;

Abstract
In this article, we show that if a semi-Riemannian space form carries a conformal vector field V of which the tangential part $\small{V^T}$ on a connected hypersurface $\small{M^N}$ ecomes a conformal vector field and the normal part $\small{V^N}$ on $\small{M^N}$ does not vanish identically, then $\small{M^N}$ is totally umbilic. Furthermore, we give a complete description of conformal vector fields on semi-Riemannian space forms.
Keywords
totally umbilic hypersurface;space form;conformal vector field;
Language
English
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1.
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